Inductive work better than a BL Touch so there's really no reason to replace it with a flimsy mechanical device that will be rattled around at 10k accel. It's also inherently more sensitive to heat just because of the design : the probe itself is a long narrow stick of plastic that will expand enough that it can be an issue...
As an
example (not saying this is representative of a BL-touch, this is just to get our gut feelings adjusted), assuming a stick length of 15mm, a CTE of 80*10-6/°C and a rise in temperature of 40C, the stick will get ~0.048mm longer which is an order of magnitude higher than the smallest Z adjustment you'd want to make.
The reason why this thermal expansion is an issue here and not the one on the nozzle (like when using a bed Z-probe (V2.4 stock) or nozzle probe (TAP)) is that plastic expands much more than metals : The same 15mm stick in a basic steel would only get ~ 0.0078 mm longer.
Personally, I still think the inductive probe is the easiest solution to implement. It will probably have a similar thermal drift as a BL-Touch but is much more robust/reliable (assuming you're using a genuine Omron probe not a clone or off-brand).
But it will have thermal drift, just like a BT-touch. To solve this I agree with
@Kermit : just go TAP, it's such a neater solution compared to the complicated clicky-style designs.